The buckling of functionally graded truncated conical shells under dynamic axial loading

• Published in: Journal of sound and vibration Vol. 305; no. 4; pp. 808 - 826
• Main Author: Sofiyev, A.H.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 11.09.2007; Elsevier
• Subjects: Buckling; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Distributed load; Vibration; Volume fraction; Conical shell; Revolution shell; Dynamic buckling; Runge Kutta method; Modeling; Uniform load; Functionnally graded material; Dynamic stability; Truncated shape; Galerkin method; Axial load; Dynamic load
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2007.05.002

The dynamic buckling of truncated conical shells made of functionally graded materials (FGMs) subject to a uniform axial compressive load, which is a linear function of time, has been studied. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the dynamic stability and compatibility equations of functionally graded truncated conical shells are obtained first. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equation with variable coefficient and critical parameters obtained using the Runge–Kutta method. The results show that the critical parameters are affected by the configurations of the constituent materials, compositional profile variations, loading speed variations and the variation of the shell geometry. Comparing the results of this study with those in the literature validates the present analysis.